Particle Size Distribution

Particle size is a vital parameter for calculating particle hydrodynamics in dispersed multiphase flows.

For example, in flows where the particles in the dispersed phase are bubbles, the size of the bubbles can change continuously due to breakup and coalescence. As interfacial transfer terms are related to the surface area of the dispersed phase, it is essential to account for the particle size and its distribution to correctly simulate the multiphase flow behavior.

The S-Gamma model, based on the work by Lo and Rao [505] and Lo and Zhang [507], is an established model for predicting particle size distribution. The model assumes a log-normal distribution of particle sizes and is based on predicting the transport of the moments of the particle size distribution:

  • Zeroth moment: the particle number density.
  • Second moment: related to the interfacial area density.
  • Third moment: related to the dispersed phase volume fraction.

The Discrete Quadrature S-Gamma model for MMP in Simcenter STAR-CCM+ solves for the zeroth and second moments. As the third moment is based on the dispersed phase volume fraction, it can be derived from the volume fraction equation that is solved by the Segregated MMP solver. The model evaluates the integrals associated with the breakup and coalescence using an adaptive discrete quadrature method. The integration points are distributed log-normally with the appropriate zeroth and second moments. Extensions to the Discrete Quadrature S-Gamma model can be supplied using the source terms for the zeroth and second moments.

Additional models are provided to account for breakup and coalescence of particles as they interact with each other. These models are selected on the multiphase interaction node for a pair of phases. The log-normal size distribution is defined by a mean particle diameter and its variance. The mean particle diameter is always updated in the calculation. The variance is updated only when breakup and/or coalescence is active.

Additionally, the S-Gamma model provides the S-Gamma Entrainment phase interaction model for simulating entrainment of bubbles or droplets in free surface flows. In multiple flow regime situations, a new dispersed phase can be generated due to physical phenomena such as breaking waves or plunging jets. The S-Gamma Entrainment model calculates the rate at which gas or liquid are entrained and the size distribution of the bubbles or droplets that form.

See Discrete Quadrature S-Gamma Model Reference.

S-Gamma Breakup Model

For breakup, the S-Gamma model considers the balance between disruptive forces (due to shear and turbulence) and restoring forces (due to surface tension) on the particle (such as a droplet). In laminar flows, the viscous effects dominate hence this regime is named “viscous breakup”. In turbulent flows, the interactions with turbulence eddies dominate and this regime is named “inertial breakup”.

See Discrete Quadrature S-Gamma Phase Interaction Model Reference.

S-Gamma Coalescence Model

For coalescence, the S-Gamma model considers the probability of collisions of the particles (such as droplets), the contact time of two colliding particles and the drainage time of liquid film between the particles. Similar to the breakup model, there is the “viscous collision” (or viscous coalescence) regime and the “inertial collision” (or inertial coalescence) regime. The drainage time is a function of the state of the particle surface, whether it is fully or partially mobile or immobile. The model therefore considers the breakup and coalescence processes in great detail.

See Discrete Quadrature S-Gamma Phase Interaction Model Reference.

S-Gamma Entrainment Model

The S-Gamma Entrainment model models the size distribution of newly created bubbles or droplets. The methods for modeling bubble entrainment are based on the balance of bubble creation energy and turbulent dissipation at the free surface. The S-Gamma entrainment model accounts for the creation of the new dispersed phase by first identifying the large scale interface, followed by identifying the high turbulent dissipation rate cells at the interface. Bubble entrainment is permitted when the turbulent dissipation rate at the large scale interface reaches a specific critical value, determining the upper and lower bound of the bubble radius. A user-defined method for droplet or bubble entrainment can also be implemented using field functions. The S-Gamma Entrainment model predicts a single mean value for nucleation per cell, but the value can vary within the domain.

See Discrete Quadrature S-Gamma Phase Interaction Model Reference.